Other Math Archive: Questions from May 17, 2023
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Dejar
T : R 3 → R
3
Sea una transformación lineal tal que
T (1, 0, 0) = (2, 4, −1), T (0, 1, 0) = (3,
−2, 1),
y
T (0, 0, 1) = (−2, 2, 0).
Encuentra la imagen indicada.
V (2, −4, 1)
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Dejar
T : R 3 → R
3
Sea una transformación lineal tal que
T (1, 1, 1) = (4, 0, −1), T (0, −1, 2) = (−5,
5, −1),
y
T (1, 0, 1) = (1, 1, 0).
Encuentra la imagen indicada.
T (4, 2, 0)
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Determina si la relación dada es una relación de
equivalencia en {1, 2, 3, 4, 5}. Si la relación es una relación de
equivalencia, liste las clases de equivalencia. x, y ∈ {1, 2, 3, 4,
5}.)
6. {(
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4. For \( x, y \in \mathbb{R} \), define \[ \begin{array}{c} d_{1}(x, y)=(x-y)^{2}, \\ d_{2}(x, y) \sqrt{|x-y|}, \\ d_{3}(x, y)=\left|x^{2}-y^{2}\right|, \\ d_{4}(x, y)=|x-2 y|, \\ d_{5}(x, y)=\frac{|
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